In case anyone else is having this happen, I'll explain what the problem was and how it got fixed.
Turns out I had used the same ID for
Advanced tab > Menu Tag ID. I had done this to try to simplify my own CSS that I was applying to these sidebar menus. Although I didn't have more than one Accordeon menu on the same page together, it still created a conflict site-wide so I was getting repeats.
To fix the problem, I created unique Menu Tag IDs for each menu. I then had to specify all of my own CSS with each of the unique IDs. Quite a bit of work (8 Accordeon menus site-wide!) but it works.
Thanks CEd!
Wendy